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A CRITIQUE OF PROFESSOR WIRTH'S METHODS 
OF MEASUREMENT OF ATTENTION 



By t,. R. GeiSSLBR 



I have been working, for the past two years, upon the problem of 
the measurement of the degree of attention; and I have sought to ap- 
proach the problem in the way that has already led to success in the 
case of intensity of sensation, by the assignment of numerical values 
to introspectively differentiated degrees of clearness. The problem 
has already been attacked by experimental psychologists, and notably 
by Professor W. Wirth, of Leipzig. Wirth's methods are entirely dif- 
ferent from my own: but his general formulation of the problem, as 
that of measurable degrees of clearness, is the same. As I have found 
Wirth's articles both difficult and obscure, and as my criticism of his 
work must be given with some fullness if it is to be itself intelligible, 
I have thought it well to devote a special paper to the discussion of 
his contributions to the subject. 

There is a difficulty at the outset, due to the fact that Wirth ex- 
presses himself only incidentally as to the relation of the field of 
attention to the field of consciousness. Wundt has made ns familiar 
with the distinction between attention and inattention, apperception 
and perception, inner point of regard and inner field of regard. Wirth, 
on the other hand, appears (although I wish to speak on this point 
with great caution) to identify the range of attention with the range 
of consciousness. He aims to give "a precise determination of the 
range of simultaneous mental processes." ] The title of his article in 
the Wundt Festschrift is "Zur Theoriedes Bewusstseinsumfanges und 
seiner Messung." He speaks of the "Versuch einer Wiedergabe des 
gesammten Bewusstseinsumfanges." 2 Phrases like these seem to 
show at least that he is concerned with a total simultaneous con- 
sciousness, with both focal and marginal processes, even if they do 
not in themselves show that he draws no definite distinction between 
centre and periphery of consciousness. But we find, later, a passage 
like this: "the mere determination of the possible number of (tachis- 
toscopically) isolated elements in maximal clearness does not at all 
show how high the absolute clearness-degrees may rise, or how many 
objects of the same clearness may be added to the average number of 
five isolated single objects, provided that all of them together form a 
familiar, associatively related whole." 8 Or again: "our measure of 
range really presupposes only a uniformly graded and highest possi- 
ble average clearness of the whole complex. 4 " Here we have, appar- 

^■Pkilosophische Studien, xx, 489. 

*Op. tit., 493. 

'Op. tit., 524. "Durcb die Feststellungder moglicben Zahl derartig (tachistosko- 
pisch) isolirter Elemente in maximaler Klarheit ist jedoch noch gar nichts dariiber 
bestimmt, wie hoch sich nun die absoluten Klarheitsgrade belaufen bezw. wieviele 
Objekte noch in der gleichen Klarheit wie bei ca. 5 isol irten Einzelobjekten zu 
diesen hinzutreten konnen. wenn sammtliche Objekte zusammen ein gelaufiges, 
untersich associativ verbundenes Ganzes ausmacben." 

*Ofi. til , 524. "Zunachst ist ja eigentlich nur die gleichmassig abgestufte und im 
Mittel moglichst erhohte Klarheit des gesammten Complexes zu unserer Messung 
des Umfanges vorausgesetzt." 



MEASUREMENT OF ATTENTION 121 

ently, an identification of attention and consciousness. And this 
inference is borne out by a passage in which Wirth discusses the rela- 
tion between the apperceptive and perceptive regions of a simultane- 
ous consciousness, and declares outright that there is no sharp 
difference between the two, but that on the contrary there are a num- 
ber of transitional stages as we pass from the higherto the lower level. 
It is evident, he says, to unaided introspection "that the contraposi- 
tion of an apperceptive and a perceptive region is not to be thought 
of as a mere dual division of consciousness. Within the simultaneous 
whole, several stages of attention and of clearness may always exist 
side by side, according as at any moment a larger or smaller number 
of unitary complexes forms the immediate experience of the subject. 
Although under certain conditions, which favor a kind of dual divi- 
sion, it is possible that a region, to which a fairly uniform attention 
is given, may be opposed to a 'background' or 'periphery' of con- 
sciousness, to which attention is as uniformly denied, nevertheless 
the concept of apperception ordinarily denotes a general direction of 
the process which goes on over the whole field, though at different 
places with unequal completeness." 1 Apperception is thus, as it 
seems, simply a general tendency to conscious self-realization, com- 
mon to all the contents of a consciousness, but carried farther in the 
case of certain mental processes than in that of others simultaneously 
present. The antithesis of 'dunkel bewusst' and 'klar bewusst' practi- 
cally lapses, as antithesis, and the difference between perception and 
apperception becomes merely a matter of degree. If it is objected 
that, even in Wundt himself, this difference ha§ never been anything 
more, we reply that while the objection may be formally sound, in 
terms of a strict definition of the conscious states known as clear and 
obscure, nevertheless the distinction has played so important a part 
in the Wundtian system as to be, to all intents and purposes, a dis- 
tinction of kind. This generic, Wundtian difference seems to be given 
up by Wirth, without defence or discussion; and we may add that 
Wundt himself, in his brief discussion of Wirth's experiments, 2 vacil- 
lates between the expressions 'range of consciousness' and 'range of 
attention' as if he too saw no reason to distinguish them. 

The question at issue, however, is more than a question of personal 
belief or of an individual psychological system; it is a question of fact, 
of observation. That Wirth would have done well to face it as a ques- 
tion of fact will come out, I believe, in the course of the present 
paper. The above interpretation of Wirth's attitude is offered with 
all reserve, since his language — if I understand it aright — is not always 
consistent. I turn now to a consideration of his experimental investi- 
gations. 

Of the three sets of experiments reported 8 the first is of a prelimi- 
nary character, and is of no importance for the determination of degrees 
of clearness. In these experiments, a standard visual complex of 25 

^Op. rit., 493. 'IHierbei zeigt sich vor allem noch, dass die Gegeniiberstellung 
eitier apperceptiven und perceptiven Region nicht etwa bloss als eine einfache 
Zweitheilung des Bewusstseins zu denken ist. Innerhalb des simultanen Ganzen 
sind jederzeit mehrere Stufen der Beachtung und der Klarheit neben einander 
moalich, je nach der grBsseren Oder geringeren Zahl von Kinheitsbildungen. auf 
welche sich das Subject augenblicklich im umnittelbaren Erleben bezieht. Wenn 
auch unter Umstanden in einer Art von Zweitheilung eine ziemlich gleichmassig 
beachtete Region einem ahnlich gleichmassig unbeachteten 'Hintergrunde,' bezw. 
einer 'Peripherie' des Bewusstseins gegeniiberstehen kaim, so bezeichnet doch der 
Begriff der Apperception mehr eine allgemeine Richtung des Processes, welcher 
innerhalb des ganzen Blickfeldes an verschiedenen Stellen in ungleicher Voll- 
kommenheit durchgefiihrt ist." 

sphys. Psych., IIT. 1903, 358-360. 

8 Philos. Stud., XX, 1902, 635-659; Psych. Stud., II, 1906, 30-88; A. Kastner und W. 
Wirth, ibid., Ill, 1907, 361-392, and IV, 1908, 139-200. 



122 GBISSLBR 

or less small geometrical objects was observed, with maximal atten- 
tion, until all its elements had been clearly apprehended. During a 
short interval, usually of less than a second, the complex was slightly 
varied, in one or several different places unknown to the observer. 
Then it was tachistoscopically re-exposed for another fraction of a 
second, and theobserver was asked to say whether, and if possible where, 
a change had taken place. Wirth's argument is as follows : "So far 
as, under these variable conditions, a correct judgment of difference 
remains possible, so far at least does the range of the simultaneous 
visual consciousness extend. But the difference necessary, at any 
given point, to arouse this correct judgment of difference, or in other 
words the differential limen under these special conditions of atten- 
tion, is at the same time a measure of the clearness-degree which 
obtained at that particular point in the standard complex". 1 That is 
to say, if the change made at a certain place in the complex is noticed 
during re-exposure, then the object was in consciousness at some 
moment of the primary exposure; and the amount of change needed 
to arouse notice is inversely proportional to the degree of clearness of 
the mental content. The results show that, if the complex contained 
only 12 or 13 figures, any change in them could always be judged cor- 
rectly; whereas, if the complex consisted of 25 figures, many errors 
occurred. With a momentary original exposure of a standard com- 
plex of 3 to 5 figures, changes in there-exposure field were recognized 
with correspondingly greater or less certainty. Thus the results 
confirm and extend those of previous tachistoscopic experiments upon 
the range of attention .proper. 

After this preliminary investigation, Wirth comes back to the "prob- 
lem of the completest possible determination of the range of con- 
sciousness", 2 which leads him more especially to "a quantitative deter- 
mination of the simultaneously present clearness-degrees or degrees of 
consciousness of the greatest possible number of elements". 8 Nothing 
is said of the apperceptive and the perceptive regions; and it is only by 
a close examination of the experimental methods and results that we 
shall be able to decide whether Wirth has measured different degrees 
of clearness within the apperceptive region only, or whether he is 
dealing with the whole series of assumed transitional steps between the 
upper and the lower levels of consciousness. Wirth devised a special 
apparatus, whose main features are as follows. The field of vision for 
the left eye consisted of the funnel-shaped and uniformly illuminated 
surface of a glass cone 50 cm. in diameter at the base and 25 cm. 
high. The left eye was placed at the centre of the perimetrical 
field. The whole surface was divided into 6 concentric rings, the 
peripheral ring being again divided into 24 regions, the next 
into 20, the next into 16, the next into 12, the last into 8, and 
the inner disc into four regions. Of the 84 regions thus demarc- 
ated, 37 were selected for experimentation. Tlie arrangement is 
shown in the Fig. By referenceto this schema, the point of change could 
be easily identified. The conical surface was observed continuously, 

1 Philos. Stud., XX, 593 f. "So weit sich unter den Ubrigen, bereits bekannten 
Bedingungen noch ein richtiges Unterschiedsbewusstsein bei einer soichen Varia- 
tion mit Sicherheit einstellt, so weit reicht mindestens der Umf ang des simultanen 
optischen Bewusstseins. Die Differenz aber, welche zur Erzielung eines soichen 
.TJnterschiedsbewusstseins an einer bestimmten Stelle nottawendig 1st also die Un- 
terschiedsschwelle unter diesen speciellen Aufmerksamkeitsbedingungen, ist zu- 
gleich ein Mass des Klarheitsgrades, welcher an dieser Stelle bei der Verteilung 
innerhalb des betreffenden Complexes herrscht." 

'Psycb. Stud., II, 30 f.; "die Aufgabe einer moglichst voll&tandigen Bestimmung 
des sog. Bewusstseinsumfanges." 

'Op.cit., 31.; "der quantitativen Bestimmung der gleichzeitig vorhandenen Klar- 
heitsgrade Oder Bewusstseinsgrade moglichst vieler Elemente." 



MEASUREMENT OF ATTENTION 



123 




with different distributions of attention, while by the manipulation of 
lenses and mirrors any one of the 37 regions could be gradually changed 
until its brightness was noticeably different from that of the rest. The 
first problem, then, was to establish the 'normal' differential linien for 
each region while the apex was fixated and the particular region was ob- 
served with maximal attention. If, for example, the brightness of the 
whole field of vision at a given moment was 174.5 photometric units, 
while the observer was attending to region no. 2, and if the additional 
brightness necessary for the region to become just noticeably different 
was 29 photometric units, and the duration of thechange was 6.75ff, then 

the normal limen for region no. 2 was 2 ^ x '^ = .91. The values for 

174-5 
each of the 37 regions were similarly determined. The next question 
was to find out how the normal limen was changed by varying concen- 
tration of attention, and how the changes could be made to express or 
measure degrees of clearness. To answer it, Wirth divided the normal 
limen of any given region by its 'distraction' limen, that is, by a limen 
for the same region with a prescribed direction of attention. "A com- 
parable value for the degrees of clearness (Beachtung) realized with 
a total distribution of attention over the various elements, each having 
its variously favorable position in the complex, may evidently be ob- 
tained without serious error if we divide the limen for maximal atten- 
tion to a known region of change by the liminal value (for the same 
region) resulting from the method without knowledge, that is, from 
the method employed for the determination of the range (of con- 
sciousness)". 1 Or, more explicitly: "a more delicate differential or 

1 Philos. Stud., XX, 598. "Einen vergleichbaren Werth der Grade der Beachtung, 
welche fiir eine und die uamliche Gesammtvertheilung der Aufmerksamkeit mit 



124 GEISSLBR 

variational limen will correspond to a higher clearness degree; and 
the ratio of this limen to the normal limen for the same region as 
known in advance and made the object of attention will offer the 
greatest approximation to a comparable measure of degrees of clear- 
ness." 1 Thus, to return to our previous example of region no. 2; if 
we determine its distraction limen, while attention is distributed over 

the whole area, we find the value?2-55M = 2.06. The degree of clear- 

146 4 
ness corresponding to the distraction limen 2.06 is then expressed by 
the ration 0.91:2.06. The clearness degrees for the other regions are 
determined in the same way. We thus obtain 37 different ratios, 
which are made comparable by reduction to the same basis of 100; 
e.g., in the case of region no. 2, the proportion 0.91:2.06= \ao:x re- 
sults in the value 226 as the clearness index for a totally distributed 
attention. Wirth has determined in this manner the clearness 
indices of all the 37 regions for 6 different distributions of attention, 
and has presented them in 6 different schemata of the kind shown in 
the Fig., each region containing a ratio which represents its clearness 
for a certain distribution of attention. As to the psychological inter- 
pretation of these schemata, he says simply: "the value of these 
diagrams is quite independent of our psychological interpretation, 
which might, e.g., be given as well in terms of purely dispositional 
factors." 2 Nevertheless, he certainly assumes that the numerical 
values of the schemata are, in some way and to some extent, definite 
quantitative measures of degrees of clearness. In order, then, to de- 
termine whether and in how far the results may be accepted as indi- 
cations of differing clearness-degrees, we must examine the diagrams 
more closely. And we begin by considering them, so far as possible, 
from what we conceive to be Wirlh's own point of view. 

Wirth gives, first, a schema of minimal normal values, 8 which he 
employs for the calculation of the ratios with the six different distri- 
butions of attention. We should expect that these values would show 
normal characteristics as regards their magnitude, their relative fre- 
quency, and their spatial distribution. Now the lowest of them is 74, 
the highest 173, the general average 119, and the mean variation 19.3. 
The most frequent values (11) occur between 91 and 99, while 26 (or 
almost three-fourths of the 37) occur within the limits of 74 and 116, 
and the 11 highest values range between 123 and 173. The most regu- 
lar spatial distribution is evinced by the four quadrants constituting 
the three innermost and complete concentric areas, and consisting of 
24 regions. The left lower quadrant has the lowest average value, 
89±5, and the right upper quadrant the highest, i26±7; the other 
two are nearly equal, ioo±7 and io2±7 for the left upper and right 
lower quadrants respectively. However, if we look at the extreme 
values in each of the five concentric areas, we find that they range, as 
we travel in the centrifugal direction, between 91 and 107, 74 and 137, 87 

verschieden giinstigerStellung der einzelnen Uleinente zu Theil werden, gewinnt 
man dann offenbar ohne grossen Fehler, wenn nian den Schwellenwerth bei maxi- 
maler Beachtung der wissentlich variirten Stelle mit dem Schwellenwerth dividirt, 
der beiunwissentlichem Verfahren, also den eigentlichen Umfangsbestimmungen, 
gewonnen worden ist." 

l Psychol. fitud., II, 31. "Dem hBheren Klarbeitsgrade wird hierbei eine feinere 
Unterschieds- bezw. Veranderungsschwelle entsprechen, deren Verhaltniss zu 
der 'Normalschwelle' fur die Veranderung des namlichen ira voraus bekannten und 
maximal beachteten Elementes die grosste Annaherung an ein vergleichbares Mass 
des Klarheitsgrades bieten diirfle." 

*0p. ctt., 73. "Der Wert dieser Karten ist ganz unabhangig von unserer psycholo- 
gischen Deutung, die z. B. auch im Sinne rein dispositioneller Verhaltnisse erfolgen 
kSnnte." 

s Op. cit., 71, Fig. 8. 



MEASUREMENT OF ATTENTION 



125 



and 137, 97 and 150, and 123 and 173. The difference in the central area 
is the smallest (16), in the next area the largest (63), and in the other 
areas nearly equal (about 50). In spite of these irregularities, Wirth 
thinks that "there appears, after all, to be a sufficient degree of uni- 
formity in the minimal values "'to warrant their use as 'normal' 
values. He therefore proceeds to divide them by the 222 distraction 
values, obtained with the six different directions of attention. It is 
obvious, however, that, if the normal values themselves show so little 
regularity, the 222 ratios partly depending upon them must be still 
less uniform as regards magnitude, relative frequency and spatial dis- 
tribution. Besides, they are further affected by the fact that, while a 
certain part of the visual field is fixated, and another part observed 
with greatest concentration of attention, a liminal change of bright- 
ness may be expected in any possible region. Surely, such complica- 
tions do not promise very satisfactory results. We find, in fact, that 
of the 222 values the lowest is 86, the highest 216. The extremes occur 
in the parts attended to as well as in those distracted from. For con- 
venience of comparison we have arranged the figures in Tables I and 
II under the heading Range. The second table differs from the first 
in having the 9 high values above 200 eliminated. If, now, these 

TABLE I 



Attention to — 


Total Field of 

Vision 
Range A v. MV. 


Area Attended 

TO 

Range av. MV. 


Area Distracted 

from 
Range Av. MV. 


Total Field 


108-284 


165 3° 


108-284 


165 30 


— 


— — 


Left Half of Field 


86-181 


131 23 


86-181 


130 24 


88-178 


131 20 


Right Half of Field 


106-186 


136 17 


T 10-173 


136 20 


106-186 


136 16 


Left Upper Quadrant 


103-206 


138 20 


103-171 


127 18 


105-206 


142 20 


Left Upper Periphery 


91-302 


147 28 


135 


— — 


91-302 


148 28 


Fixation Point 


93-162 


"3 15 


— 


— — 


93-162 


123 15 



TABLE II 



Attention to — 


Total Field op 

Vision 
Range av. MV. 


Area Attended 

to 
Range Av. MV, 


Area Distracted 

from 
Range av. MV. 


Total Field 


108-200 151 19 


IO8-2O0 


151 19 


— 


— — 


Left Half 


86-181 131 23 


86-181 


130 24 


88-178 


131 20 


Right Half 


106-186 136 17 


I IO-I73 


I36 20 


106-186 


136 16 


Left Upper Qu. 


103-198 136 19 


103-171 


117 18 


105-198 


140 19 


Left Upper Per. 


91-192 141 22 


135 


— — 


91-192 


141 22 


Fixation Point 


93-162 123 15 


— — 


— — 


93-162 


t23 15 



l 0p. cit., 72. "So ist schliesslich cine hinreichende Gleichmassigkeit der Minimal- 
werte vorhanden." 



126 GEISSLBR 

values are really expressions of degrees of clearness, we should expect 
to find a marked difference in their distributions; the low values ought 
to be found in the parts attended to, the high values in the other parts 
of the field. Or, if unknown and occasional errors or the irregularity 
of the normal values be allowed for, we should still expect to find the 
average values for the parts attended to lower than those for the rest 
of the field of vision. 

The tables show no sign of such a distribution. Wirth himself ex- 
plains the disappointing character of the results as follows: "the effort 
of the special activity to bring about the right distribution of atten- 
tion makes itself felt as a competitive factor. With distribution of 
attention over the whole field, it is probable that the lowering of the 
clearness values is for the most part due to this disturbing factor. 
But the distribution of attention to a certain region also carries with 
it the possibility that a higher clearness-degree may be assigned to 
some particular point which, under the circumstances, happens to be 
the object of maximal attention. [For these reasons] the arrangement 
of the values within the observed area gives no constant picture of a 
determinate clearness-relievo in the visual field under steady fixa- 
tion." 1 Such an admission seems, however, to be fatal to the whole 
investigation. If the difficulties encountered were so great as entirely 
to obscure the results, then the experimental method employed is not 
applicable to the problem in hand. 

The third set of experiments upon clearness-degrees is reported by 
A. Kastner and W. Wirth. Here recourse is had, not to just notice- 
able brightness differences, but to a plainly supraliminal brightness- 
change. The clearness-indices are expressed by the times of quickest 
possible reaction to the discrimination of change. Otherwise the ex- 
perimental arrangements remain the same as in the previous work. 
The following groups of experiments were made: I a, simple reaction 
with knowledge of the region to be changed and maximal concentra- 
tion upon it (to furnish a series of 'normal' reaction times correspond- 
ing to the normal brightness determinations in the former investiga- 
tion); I b, complete reaction, without knowledge, and with attention 
distributed over some one quadrant; I c, the same with total distribu- 
tion of attention; II, the same, with attention upon a region in the 
left upper periphery; III, selective reaction without knowledge, at- 
tention being totally distributed, and the reacting forefingers being 
assigned either to the right and left halves of the visual field, or else 
the one to a particular region and the other to all other regions. "It 
seems justifiable to assume that a proportional change in the reaction 
time will occur, if at all, then assuredly in connection with its depen- 
dence upon the degree of clearness with which the motive to reaction 
is apprehended." 2 The clearness-index is expressed by a number 
which is found by multiplying the reaction time of a given region, 
with a certain distribution of attention, by a fraction whose numera- 
tor is a constant (the average of the 37 normal values, 223.80-) and 

l Op. cit., 87. "Indessen begitint bereits die Anstrengung der besonderen Tatigkeit 
zur eigentlichen Verteilung der Aufmerksamkeit sich konkurrierend geltend zu 
machen. Bet der Verteilung auf das ganze Sehfeld fallt wahrscheinlich der Haupt- 
anteil der Erniedrigung des Klarheitswertes dieser Stoning zu. Doch tragt die 
Verteilung der Aufmerksamkeit auf ein Gebiet jederzeit die MBglichkeit in sich, 
einem beliebigen bei der Verteilung gerade maximal beachteten Punkteinen 
hSheren Klarheitsgrad zukommen zu lassen, als ohne diese Verteilung. Die Art 
der Anordung der Werte innerhalb des beachteten Gebietes lasst keine Konstanz 
eines bestimmten Klarheitsreliefsim Sehfeld bei festgehaltener Fixation auffinden." 

*Psych. Stud., Ill, 300. "Wenn irgendwo, so scheint nun gerade fur die Abhangig- 
keit der Reaktionszeit vom Klarheitsgrade der Motivauffassuug, die wir hier im 
einzelnen untersuchen wollen, eine solche proportionale Veranderung der 
zunachst von beliebigen Unterschieden der Raumlage modifizierten Reaktions- 
zeiten angenommen werden zu kbnnen." 



MEASUREMENT OF ATTENTION 1 27 

-whose denominator is the normal average value (of 5 individual 
values') for a given region. Thus, if the reaction time for region no 
18 is 2i&r. with total distribution of attention, while the normal aver' 
age reaction for the same region is 221, then its clearness-index wilj 

be 2l6x^^-=2i8. Hence, with total distribution of attention, 218 

221 
represents the degree of clearness for region no. 18, independently of 
its position in the visual field. 

The results of the normal reaction experiments are uniform. The 
times vary only between 200 and 245, and show a fairly regular distri- 
bution over the whole area. On the other hand, the results with 
various distributions of attention are so irregular that the authors are 
satisfied with the general comparison of the average values for the 
whole area, without, as a rule, giving due consideration to the large 
mean variations, or even distinguishing between the regions attended 
to and those not attended to. Their conclusion runs: "no matter 
how much the distribution of the times varies, over the whole visual 
field, for the different adjustments of attention, the general averages 
agree almost perfectly in cases of approximately equal practice; their 
mean is 282. This time is, therefore, in a certain sense the expression 
of a constant energy expended in the control of the whole perceptual 
field of possible motives to reaction, — an energy that, under the dif- 
ferent distributions of attention, manifests itself in the time of prep- 
aration even for varying spatial positions ; so that, on the average, a 
higher degree of expectation of a certain group of motives lowers cor- 
respondingly the preparedness of the observer for all the other possi- 
bilities." J It is difficult to see what relation such a conclusion can 
sustain to the problem of measuring either the range of consciousness 
or the degrees of attentional clearness. Some of the irregularities are, 
it is true, more or less adequately explained, as due to special circum- 
stances, while others are termed simply "Zufalligkeiten." 2 The latter 
designation seems to apply, for instance, to the case of total distribu- 
tion of attention, where the four regions of the most extreme concen- 
tric area contain not only the longest and the average reaction times 
of the whole series, but also the two quickest reactions of that par- 
ticular series. However, it is not of vital importance that we should 
know the reason for the numerous irregularities. The fact that they 
occur at all, and prevent the appearance of the expected results, is 
sufficient to prove the inexpediency of the method. Indeed, in their 
closing sentence, the authors virtually admit the inadequacy of the 
investigation. "Further enquiry must determine how far a more de- 
tailed differentiation of the co-ordinations, with more than two possi- 
bilities of choice, may avail to furnish a more accurate representation 
of the clearness-relievo within any given group of motives to reac- 
tion." 3 

Thus far we have sought to review Wirth's investigations entirely 
from what we regard as his own standpoint; and our conclusion is 

1 Psych. Stud., IV, 163. "So verschieden als die Verteiiung der Zeiten auf das 
ganze Sehfeld bei den verschiedenen Einstellungen der Aufmerksamkeit ist, so 
stiraraen die Gesamtmittel bei ungefahr gleichen allgemeiner Uebung fast voll- 
st'andig iiberein und ergeben im Mittel hier 282. Diese Zeit ist also gewissermassen 
der Ausdruck einer konstanlen Energie zur Beherrschung des ganzen Wahrneh- 
mungsbereiches moglicher Reizmotive, die bei den verschiedenen Verteilungen 
der Aufmerksamkeit in der Vorbereitungszeit auch in verschiedener raumlicher 
Aufteilung zur Geltung kommt; so dass die grBssere Erwartung der einen Motiv- 
gruppe die Bereitschaft fiir die Ubrigeu EventualitSten im Mittel urn eln Entspre- 
chendes herabsetzt." 

a Op. tit., 148. 

8 Op. tit., 200. "Es ware nun weiterhin zu untersuchen, inwiefern eine weitere 
Differenzierung der Zuordnungen in einer mehrfachen Disjunktion ein genauerea 
Abbild des Klarheitsreliefs innerhalb eines Motivbereiches ergibt." 



128 GBISSLER 

that he has failed to solve his problem. The difficulties of his method 
and the many factors that complicate his observations seem to obscure 
the real nature of his results and to rob them of any decisive signifi- 
cance. It may, however, be possible to give the results a new mean- 
ing by an interpretation from that standpoint which, in opposition to 
Wirth's, makes a sharper distinction between the apperceptive and 
the perceptive levels of consciousness. 

There can be no doubt that Wirth's experiments have dealt with 
certain degrees of clearness. The question is whether they covered 
the whole range of a simultaneous consciousness, from the clearest 
region of apperception to the obscurest region of perception, or 
whether they were merely concerned with certain relatively small 
differences of clearness within the level of apperception itself. Wirth 
assumes that his low values represent a high degree of clearness. He 
has to admit, however, that his high values do not necessarily repre- 
sent a low degree of clearness. They were due, at least in part, to 
distracting factors. While, therefore, the low values may possibly 
furnish a numerical statement of the clearness of processes on the 
apperceptive level, Wirth has been unable either to measure the clear- 
ness of processes on the lower level, or to prove the existence of his 
assumed transitional steps between the two levels. 

Let us consider once more the liminal brightness-determinations 
obtained with various distributions of attention. The 222 values rep- 
resent 100 actual ratios. Now Wirth certainly does not mean that 
each separate ratio measures a new degree of clearness, so that there 
are at least 100 stages between the two extremes of his experiments. 
If he had thought this, he would not have disregarded the large mean 
variations, and have contented himself with general averages. On the 
other hand, if his values do embrace the whole range of consciousness, 
and if they demarcate in a rough way some smaller number of inter- 
mediate steps, then we should expect them to fall into natural groups 
of greatest frequency, clustered around certain averages representing 
these steps, and thus to form a multimodal frequency curve. In this 
event, the number of such groups will indicate the number of inter- 
mediate steps, and the difference between their averages will be a 
rough measure of the size of the steps. But if we examine the total 
frequency distribution of the 222 values, irrespective of the various 
kinds of attention under which they were obtained, we find only the 
slightest indication of grouping between the values 90 and 160. The 
probable meaning of this we discuss later on. It is very significant 
that of the 100 different values only 

2 occurred 7 times (namely 130 and 144) 
1 " 6 " ( " 146) 

7 " 5 " ( " *°3. no. "9> I2 5> 137. !49> and 157) 
12 " 4 " 

21 " 3 " 

44 - 2 " 
Although the figures vary, as was stated above, between the limits of 
86 and 302, 90% of them (or 200 out of the 222) occur between 90 and 
180; and, what is more, 75% (or 165) lie between 90 and 160. That 
there is no multimodal distribution may be easily shown by con- 
structing a frequency surface, in which, e. g., groups of 10 possible 
values are represented in each unit of the abscissa. The same fact is 
brought out in the following table : 



MEASUREMENT OE ATTENTION 1 29 



Within the limits of 81 and 


90 there 


occur 3 cases 


9i 


a 


100 


tt 


tt 


10 


tt 


101 


tt 


no 


tt 


tt 


26 


tt 


in 


tt 


120 


it 


a 


31 


tt 


121 


n 


130 


tt 


tt 


32 


a 


131 


tt 


140 


tt 


tt 


26 


tt 


141 


U 


150 


It 


tt 


30 


tt 


151 


tt 


160 


tt 


tt 


21 


tt 


161 


tt 


170 


tt 


tt 


13 


tt 


171 


n 


180 


tt 


tt 


12 


tt 


181 


tt 


190 


tt 


a 


6 


tt 


191 


tt 


200 


tt 


it 


4 


tt 


201 


a 


30a 


tt 


tt 


9 


tt 



Thus our expectation of finding natural groups of values is not real- 
ized. We find instead that the 222 (minus the 9 extreme cases above 
200) group themselves around one general average of 136, with 75% of 
them clustering closely about 122. A similar distribution is found in 
Wirth's reaction times, as may again be seen from the construction 
of a frequency surface. This fact would seem to indicate that, during 
most of the experiments, the observer managed to maintain a fairly 
constant and fairly high degree of concentration, while during the re- 
mainder the difficulties of which we have spoken exercised a dominant 
influence upon the results. Such an assumption becomes still more 
plausible if we compare the frequency distribution of Wirth's reaction 
times with those of other experimenters upon the sensorial reaction. 
We may select for instance the results of Alechsieff as typical, since 
he also took sensorial or complete reactions to visual stimuli. 1 We 
call attention to the curves for his 4 observers A, K, F, and S. These 
observers were required to concentrate their attention maximally upon 
the stimulus. Their "Einstellung" thus differed as widely as possible 
from that required by Wirth. Nevertheless the distribution of their 
results is strikingly similar to Wirth's ; so similar that the agreement 
can hardly be due to accident. It therefore seems fair to suppose 
that Wirth, after all, maintained a uniform concentration of attention 
upon the field of vision, and that his degrees of clearness — in so far as 
they are correctly indicated by his lower values — are only small varia- 
tions upon the apperceptive level. 

With this interpretation in mind we may come back to the slight 
indications of grouping between 90 and 160. Near our corrected 
average value of 122 there is, as has been said, a relatively large fre- 
quency of similar values. We notice further, small groups at no 
and 103, where we may perhaps assume slight rises in clearness above 
the common or normal level. We notice also small groups at the 
lower values 128, 137, 146, and 156, which in a similar way we may 
perhaps assume to represent slight decreases of clearness. The same 
thing appears on inspection of the reaction times. It is true that we' 
are not here dealing with simultaneity in consciousness, since the 
values are taken from the different distributions of attention. And if 
separate curves are drawn for the separate distributions, they will be 
found to show both fewer and less marked deflections from their 
general apperceptive levels (especially in the case of the brightness- 
values, where all values above 160 should probably be eliminated). 
It would plainly be wrong, then, to lay any great emphasis upon these 
groups, in view of the extreme complications of Wirth's experimental 
conditions. They are at best, only very slight, and are mentioned 
merely in order to do full justice to the results. 

1 Philos. Stud., xvi, 1900, 1 ff. 

9 



130 GBISSLKR 

All these considerations force upon us the conclusion that Wirth's 
numerical values, in as far as they may be admitted to measure degrees 
of clearness, refer to slight clearness variations on the apperceptive 
level only; that he has not measured the range of a total conscious- 
ness; and that he has given us no evidence of the existence of transi- 
tional degrees or steps between the apperceptive and the perceptive 
level. It may be added that, so far as can be seen without repetition 
of the experiments, Wirth's experimental arrangements were most 
unfavorable to a solution of his problem. All tachistoscopic experi- 
ments (and the conical field is, in essentials, tachistoscopic) tend to 
exaggerate the difference between the two main levels of conscious- 
ness. Under Wirth's conditions, the whole world of extraneous 
lights and colors was, objectively as well as subjectively, excluded 
from the observer's eye and mind. The difficulties of concentration 
of attention upon the various parts of the visual field, with mainte- 
nance of a constant fixation, must have required an almost hypnotic 
state of attention, in which the isolated tachistoscopic objects appealed 
to the observer with such exclusive force that the mental processes 
which would normally have occupied the perceptive level were driven 
towards or below the li men of consciousness. This is probably Wirth's 
justification for their neglect. But such an extreme and almost ab- 
normal state of attention is, evidently, not the most favorable condi- 
tion for the solution of his problem, in whatever form he meant this 
problem to be understood. It is too far removed from the conditions 
of daily life, where the most natural and frequent occurrence seems 
to be the more or less clear apperception of a single mental process or 
small unitary group of processes, upon a background of other, more 
or less obscure but still noticeable mental processes. 

There are one or two other points that call for criticism. In the 
first place, practically the only observer, especially in the last two 
sets of experiments, was Wirth himself, so that there is no possibility 
of comparing results obtained from different individuals. The excuse 
offered is lack of time which, however, can hardly be accepted as 
valid. In the second place, comparison is the more necessary in this 
case since it is practically impossible to repeat the experiments any- 
where except in the Leipzig laboratory. And yet they must be 
repeated, unless we agree that the methods are so faulty and so un- 
promising as to spare us the necessity of repetition. This, at any 
rate, is clear: that Wirth has failed to solve his problem. For, if we 
try to interpret his numerical values from his own standpoint, we find 
them meaningless; they are obscured or invalidated by complicating 
factors. And if we look at them from our own point of view, and 
eliminate into the bargain all doubtful cases, they appear to disprove 
his assumption of the existence of transitional steps between the ap- 
perceptive and perceptive levels. The main reasons for his failure 
seem to be uncertainty and ambiguity in the formulation of the prob- 
lem ; the impossibility of overcoming difficulties of observation ; and 
the restricting conditions of his experimental arrangement, which was 
rather unfavorable than favorable to the type of consciousness under 
investigation.